It has been a few years now since I first seriously started looking for and writing about a ski boot that would climb well. The original TLT5 was a decent climbing boot. But easily bettered as a ski boot. Hence the TLT6. TLT6 is still likely the bench mark for a cross over boot.
PDG and the Scarpa Alien 1.0 will work well enough if it isn't too cold, the climbing not super hard and most importantly, the boot fits you well. Other wise either will eat your feet up pretty quickly in my experience as will the TLT6!
PDG and a good mate for the boot, a Grivel G20 on easy mixed in Chamonix